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From maps to graphs and back, from life to death and eternity?

Wednesday, April 19th, 2017

[ by Charles Cameron — graphs and networks, life and death, quality and quantity of life, personal mortality, the (implictly immortal) trinity ].
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I was struck by these items, verbal and visual, in Numberphile‘s YouTube video, The Four Color Map Theorem. The speaker introduces a simple, four color map:

Then indicates:

I’ve turned that map into a network:

The question, can this map be colored using four colors, or better? is the same question as saying, can this network be colored using four colors, or better?

There are things we can learn now about maps, by studying networks instead. .. By studying networks, we can study all the different kind of maps. Now, all maps make networks, but not all networks make valid maps.

Given that my HipBone game boards are graphs — my games as played are conceptual graphs — I’m always on the lookout for easily digested gobbits of graph theory to see if they’re applicable to my games, or to put that another way, whether they can startle me into any new insights.

  • At least some HipBone games could be played on maps..
  • **

    One could thus view maps of the various sectarian interests in play in the Levant / Shams — theologies onto geographic areas, Alevi, Twelver, Salafi, Salafi-jihadist, Yezidi, Druze, Christian etc — as conceptual maps analogous to conceptual graphs.

    And these conceptual maps are important in terms of strategy.

    Different graphs could be obtained by articulating the linkages between different sects and ethnicities, eg Turkomen with Turks, Alevi and Ismaili with Twelver Shiism, and Shia with Sunni vs (eg) Christian.. and switching back and forth between map and grapoh might then prove suggestive, instructive..

    **

    Once started on Numberphile’s math-curious videos it can be hard to stop.. Here’s a surprise from the third such video I chased thids afternoon, the one on The Feigenbaum Constant:

    Life and Death can be mathematized!

    I think that diagram — if it can be believed — answers the vexed issue of quality and quantity, and possibly also the hard problem in consciousness.

    **

    I naturally attempted to place myself on the implicit timeline between Life and Death on that diagram. I’m reasonably far along (minor stroke, check, triple bypass, check, on dialysis, check, etc), and, shall we say, somewhat aware of my mortality.

    Someone get me a slide-rule, I’d like to calculate the precise.. unh, on second thoughts, maybe not.

    **

    The only happily viable move from here — I believe — is to infinity, so let’s go.

    My games, I’d suggest, make a contribution to graph theory. Specifically, to that branch of graph theory in which Margaret Masterman was a pioneer, is the area of conceptual graphs, which I meantioned above. Indeed, the (theo)logical icon Masterman explored with her Benedictine Abbess friend as described in Theism as a Scientific Hypothesis (part 1), Theoria to Theory Vol 1, 3rd Quarter, April 1967, pp 240-46:

    visiting it in Boolean terms:

    is none other than the graph used as an exemplar of the map-graph correlation in the Numberphile video, second illustration at the top of this post.

    **

    In the Trinitarian version of this graph, however, two kinds of “edge” or linkage are required: for the links between individual Persons (“non est”) and the links between Persons and Godhead (“est”).

    And the same is true, interestingly enough, with even more types of linkage, in Oronce Fine‘s (entirely secular?) map of the elements:

    **

    And that’s enough thinking for one day, perhaps. We shall see..

    Mes Aynak, Afghanistan, the equation

    Monday, April 10th, 2017

    [ by Charles Cameron — a question of value ]
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    **

    Footprints: Saving artefacts in Afghanistan

    The Buddha rests quietly in a corner of the National Museum of Afghanistan.

    While a group of Afghan restorers — with more than four decades of experience between them — work to restore similar artefacts, the Buddha, dating back to at least the second century BC, sits cross-legged, arms folded, awaiting its public debut in the city.

    The statue, set to be unveiled to the public in the coming weeks, is a testament to the rich history of a nation that has seen various empires and conquerors pass through its land.

    “There are artefacts in every corner of this country,” said Fahim Rahimi, the director of the National Museum of Afghanistan. However, even the layers of sand, silt and time have not been able to keep these artefacts safe from the forces of conflict and capitalism.

    [ .. ]

    The Buddha itself, discovered near the nation’s largest copper mine, is an embodiment of the duelling threats facing the physical remnants of Afghanistan’s cultural history. The statue, sitting in a reconstructed stupa, was found in 2012 in the Mes Aynak area of the eastern province of Logar. Mes Aynak, meaning literally “the little copper source,” is home to a 2,000-year-old Buddhist city filled with ancient statues, manuscripts, frescoes, shrines and stupas. It is also at the centre of a $3billion Chinese mining contract signed in 2007.

    **

    William Bruce My NameSake and presumed Clansman Cameron wrote “Not everything that can be counted counts, and not everything that counts can be counted.”

    Equation implies equals. Here we have a tug of cash-and-peace.

    Trump, Flynn and immunity

    Friday, March 31st, 2017

    [ by Charles Cameron — tweets, and how they become, for me, a problem in number theory ]
    .

    The initial question is, should I pair this:

    with this:

    Or this:

    — or the last two with each other?

    Such are the hazards of imprisonment within the DoubleQuote system — two, when three or more are available and relevant, becomes a constraint rather than a facilitation. So would any other positive integer — and god save us from the irrationsals!

    A couple or so couples

    Saturday, February 18th, 2017

    [ by Charles Cameron — gathering these things the way an obsessed squirrel gathers nuts ]
    .

    I’d say there’s nothing more thought-provocative than running across an unexpected parallelism or opposition — and the closer the parallel the better. Once thought has been provoked, though that’s just the starting point — it needs to run its course with the appropriate caution and rigor. Here, then, are some parallelisms I’ve run into recently, for your provocation.

    **

    The Dilletante’s Winterings, Michael McFaul’s easy, broken parallel:

    Michael McFaul, the former US ambassador to Russia, has a blog on the site of Ekho Moskvy, the independent radio station based in Moscow. Commenting on the appointment of Steve Bannon to the National Security Council, he wrote:

    It’s the equivalent of Putin appointing Alexander Dugin to the [Russian] Security Council and telling generals Bortnikov [head of the FSB] and Gerasimov [head of the general staff] to only attend when they are needed.

    **

    Craig Whiteside (2016) The Islamic State and the Return of RevolutionaryWarfare, Small Wars & Insurgencies, 27:5, 743-776, DOI: 10.1080/09592318.2016.1208287:

    This paper starts by comparing the Islamic State to the Vietnamese communists in a revolutionary warfare framework..

    I didn’t find a single-sentence assertion of this parallelism, not am I expert in revolutionary warfare — but manynof our readers here on Zenpundit are, so I’ll leave the critical appraisal of this proposition to you-all..

    **

    Defense One, So, American Mass Shooters and Islamic Terrorists Do Have Something in Common:

    Like radical Islamic groups, white supremacist and other right-wing terrorist groups offer people (especially men) who feel isolated and disempowered a chance to feel important and welcome. It’s the same psychological phenomenon, different culture war. And thus the KKK gains new recruits along with ISIL.

    **

    And for good measure… not, you understand, that I understand it —

    Metod Saniga, Algebraic Geometry: a Tool for Resolving the Enigma of Time?

    An illustrative example of such a temporal dimension is provided by a specific linear, single-parametric set (so-called pencil) of conics in the projective plane. This set of conics is found to nicely reproduce the experienced arrow of time when the projective plane is affinized; it simply suffices to postulate that each proper conic of the pencil stands for a single temporal event, and relate three distinct kinds of (proper) affine conic, viz. a hyperbola, a parabola and an ellipse, with the three different kinds of temporal event, viz. the past, present and future, respectively..

    Time, as St Augustine noted, makes sense — until you try to figure out what sense it makes.

    It’s easier to accept John Nash than the goddess Namagiri

    Saturday, January 7th, 2017

    [ by Charles Cameron — delighted to find Ramanujan is not alone in dreaming of mathematics ]
    .

    When the Hinduism Today writer above says people found Ramanujan‘s assertion that his equations were given him in dreams by the local goddess Namagiri “irksome” he was understing the case: many mathematicians are allergic to the idea of a goddess providing inspiration to a mathematician in a devotional dream state. Thus Krishnaswami Alladi, in his Review of the Movie on the mathematical genius Ramanujan, writes:

    The legend is that the Hindu Goddess Namagiri came in Ramanujan’s dreams and gave him these formulae..

    See? It’s a legend, a priori, since “goddesses” don’t exist.

    John Nash, he of the Beautiful Mind, game theory equilibria, and the Nobel Prize, on the other hand — if he provides inspiration to a fellow mathematician in a dream?

    Why, his solution can be acknowledged as such in a learned paper..


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